tag:blogger.com,1999:blog-4912713243046142041.post4665833685241367582..comments2024-03-28T12:17:44.126-05:00Comments on TYWKIWDBI ("Tai-Wiki-Widbee"): Proof that -1 is positiveMinnesotastanhttp://www.blogger.com/profile/01382888179579245181noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-4912713243046142041.post-89391351142909510542016-05-24T00:08:33.019-05:002016-05-24T00:08:33.019-05:00but S isn't positive is it nowbut S isn't positive is it nowMark Masonhttps://www.blogger.com/profile/06038170191498529415noreply@blogger.comtag:blogger.com,1999:blog-4912713243046142041.post-23440076662102975612012-09-10T13:46:41.073-05:002012-09-10T13:46:41.073-05:00which infinity?
which infinity?<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4912713243046142041.post-21110730813565979472009-11-09T18:50:09.680-06:002009-11-09T18:50:09.680-06:00For me the simplest "disproof" is not a ...For me the simplest "disproof" is not a mathematical one, but a logical one - that two times infinity is nonsense.Minnesotastanhttps://www.blogger.com/profile/01382888179579245181noreply@blogger.comtag:blogger.com,1999:blog-4912713243046142041.post-65428622520427914052009-11-09T15:25:49.201-06:002009-11-09T15:25:49.201-06:00So what you're saying is that
S = summation...So what you're saying is that<br /> S = summation of 2^n from 0 to some term<br />Let's assume that this term is not infinity. Which would mean that<br /> S = 2^(n+1) - 1<br />Now manipulating this equation for both cases<br /> 2S = 2^(n+2) - 2<br /> S - 1 = 2^(n+1)<br />Now, lets find some terms that will show that 2S and S - 1 are equal<br /> 2^(n+2) - 2 = 2^(n+1)<br /> => 2^n = 1<br />The only possible term that will prove this is 0. Therefore, your proof of -1 being a positive number is disproven, due to the fact that the term is obviously not 0, but closer to infinity. I hope that makes sense? Just another look at how this isn't possible.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4912713243046142041.post-79704636089484993032008-12-22T20:43:00.000-06:002008-12-22T20:43:00.000-06:00Aha, I think Mike has the official mathematical re...Aha, I think Mike has the official mathematical reasoning behind it. I can sleep tonight.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4912713243046142041.post-41966684931745770632008-12-22T12:44:00.000-06:002008-12-22T12:44:00.000-06:00It's simple. Based upon the first result, S is eq...It's simple. Based upon the first result, S is equal to infinity, and therefore is not a rational number, and cannot be treated as such. But, it's still fun to mess with stuff like this.Mikehttps://www.blogger.com/profile/14797317910988407423noreply@blogger.comtag:blogger.com,1999:blog-4912713243046142041.post-84981113397555133742008-12-22T08:38:00.000-06:002008-12-22T08:38:00.000-06:00I'm an English major, so I'm on even shakier groun...I'm an English major, so I'm on even shakier ground than you are, but let me try to address your argument.<BR/><BR/>As you point out, we're dealing with infinitely long series.<BR/><BR/>You've demonstrated that the series 2S and S diverge by subtracting one from another. <BR/><BR/>Instead of doing that, create a third series - the S-1 series - by subtracting 1 from the S series:<BR/><BR/>S = 1+2+4+8+16... <BR/><BR/>Then S-1 = 2+4+8+16...<BR/><BR/>Note the 2S series is the same:<BR/>2S = 2+4+8+16...<BR/><BR/>So 2S = S-1, and simpliflying<BR/>S = -1<BR/><BR/>which is negative. But the original postulate was that it was positive, being composed only of the sum of positive numbers.<BR/><BR/>I think all that this means is that logic doesn't apply to infinite series. Using infinite series, you can prove that 4 = 3 (see this link: http://tywkiwdbi.blogspot.com/2007/12/proof-that-4-equals-3.html)Minnesotastanhttps://www.blogger.com/profile/01382888179579245181noreply@blogger.comtag:blogger.com,1999:blog-4912713243046142041.post-8548648159545633992008-12-21T22:24:00.000-06:002008-12-21T22:24:00.000-06:00There's definitely a problem here (especially sinc...There's definitely a problem here (especially since it violates the definition of a positive number). Granted, I'm a physics major, so the purer proofs are usually a bit beyond me, but take the following definitions of the series:<BR/>S=Sum(2^n) from 0 to Inf.<BR/>2S=Sum(2n)-1 from 0 to Inf.<BR/>Take the first terms, though.<BR/>2S-S=2-1=1<BR/>First two terms:<BR/>2S-S=(2+4)-(1+2)=3<BR/>First 3 terms:<BR/>2S-S=(2+4+8)-(1+2+4)=7<BR/>First 4:<BR/>2S-S=(2+4+8+16)-(1+2+4+8)=15<BR/>So it's clear that 2S-S diverges and will not converge to any value, including -1. I'm sure that there's some fancy theorem that covers this, but I'll just stick to this.Anonymousnoreply@blogger.com